Experimental comparisons among various models for the reverse annealing of the effective concentration of ionized space charges (Neff) of neutron irradiated silicon detectors

Experimental data of the reverse annealing of the effective concentration of ionized space charges (Neff , also called effective doping or impurity concentration) of neutron irradiated high resistivity silicon detectors has been compared with various models. The models include the compensation model (first order), the cluster model of the first order, the neutral to acceptor model (first order), and the cluster model of the second order. Detectors irradiated to various neutron fluences have been annealed at 80 C for up to 17 hours to reach the saturation of the first apparent stage of the Neff reverse anneal, which is equivalent of about one year of room temperature (RT) anneal. The annealing time constant, defined as the time at half saturation τ1/2, has been found to be virtually a constant (∼140 minutes±14%) for detectors irradiated to fluences ranging from 8.2x1012 n/cm2 to 3.2x1013 n/cm2, which is the distinguishing characteristic of the first order process. The least square fit of the data to the first order models has shown a time constant of 221.7 minutes with a 14% error and that to the second order model has shown a k constant of 7.3x10-5 s-1 with a 37% error. The best fit, however, is a first order fit with two time constants: short one (∼44 minutes±25%) with a small amplitude and a longer one (∼290 minutes±12%) with an almost five time larger amplitude, suggesting that even for the apparent first stage of the Neff reverse anneal, there may be two stages. There is also evidence that even after the apparent first stage anneal, there is at least another stage which is showing up in higher temperature annealing (150 C)